Recently, recording high-resolution Electroencephalograms (EEGs) from a large number of electrodes has become a clear trend in both brain research and clinical diagnosis. However, the current EEG data acquisition systems store the collected data in a form that has never changed since digital EEG emerged about 30 years ago. As a result, the size of the output data file increases enormously as the number of recording channels increases, causing various problems including high costs in data analysis, database management, archiving, and transmission through the internet. This proposal seeks to solve this problem through fundamental research on data compression specifically for EEG data, but applicable to other physiological data as well. Our key approach is based on the application of advanced mathematical and signal processing technologies to this critical problem. We will develop and optimize a variable sampling technique which eliminates redundant data samples using spline interpolation and wavelet transformation. We will also investigate lossless data compression algorithms that possess two important features: 1) any part of the data within the compressed file can be read without having to decompress the entire file, and 2) the compressed data can be transmitted and presented in coarse or fine resolutions as needed. We expect that, using both variable sampling and lossless compression, the EEG file size can be reduced by approximately 70 percent.